Abstract. We give a complete proof of the twisted duality property
$M (q)'=\tilde{Z} M (q^\perp) \tilde{Z}^*$
of the (self--dual) CAR--Algebra in any Fock representation.
The proof is based on the natural Halmos decomposition of the
(reference) Hilbert space when two suitable closed subspaces have been
distinguished. We use Modular Theory and techniques developed by
Kato concerning pairs of projections in some essential steps of
the proof